Polynomial Operations
Adding, subtracting, and multiplying polynomials
Polynomial Operations
Adding, subtracting, and multiplying polynomials
Math - Grade 9-12
- 1
Simplify: (3x^2 + 5x - 7) + (2x^2 - 4x + 9)
Combine like terms by matching the x^2 terms, x terms, and constants.
The simplified expression is 5x^2 + x + 2. - 2
Simplify: (6a^2 - 3a + 8) - (2a^2 + 5a - 1)
The simplified expression is 4a^2 - 8a + 9. - 3
Simplify: 4y(2y^2 - 3y + 5)
Distribute 4y to each term inside the parentheses.
The simplified expression is 8y^3 - 12y^2 + 20y. - 4
Simplify: (x + 7)(x + 3)
The simplified expression is x^2 + 10x + 21. - 5
Simplify: (2m - 5)(m + 4)
Use distribution or the FOIL method to multiply each pair of terms.
The simplified expression is 2m^2 + 3m - 20. - 6
Simplify: (5p^2 + 2p - 6) + (3p^2 - 7p + 4)
The simplified expression is 8p^2 - 5p - 2. - 7
Simplify: (7x^3 - 2x^2 + x - 9) - (3x^3 + 4x^2 - 5x + 1)
Change the signs in the second polynomial before combining like terms.
The simplified expression is 4x^3 - 6x^2 + 6x - 10. - 8
Simplify: -3z^2(2z - 5) + 4z
The simplified expression is -6z^3 + 15z^2 + 4z. - 9
Simplify: (n - 6)^2
Expand the square by multiplying (n - 6)(n - 6).
The simplified expression is n^2 - 12n + 36. - 10
Simplify: (3x + 2)(x - 5)
The simplified expression is 3x^2 - 13x - 10. - 11
Simplify: (4r^2 - r + 6) + (2r^2 + 9r - 11) - (r^2 + 3r + 1)
First combine the first two polynomials, then subtract the third.
The simplified expression is 5r^2 + 5r - 6. - 12
Simplify: 2t^2(3t^2 - 4t + 7)
The simplified expression is 6t^4 - 8t^3 + 14t^2. - 13
Simplify: (x^2 + 4x + 1) - (2x^2 - x + 8)
Be careful to distribute the subtraction sign to every term in the second polynomial.
The simplified expression is -x^2 + 5x - 7. - 14
Simplify: (2b - 3)(2b + 3)
The simplified expression is 4b^2 - 9. - 15
Simplify: (x + 2)(x^2 - 3x + 4)
Distribute each term in the binomial across the trinomial, then combine like terms.
The simplified expression is x^3 - x^2 - 2x + 8.